The implicit intergral method that we have already introduced in a previous paper, together with its application to the non-Local Thermal Equilibrium (non-LTE) line formation problem, is considered here for another paradigm problem, namely, the self-consistent temperature correction when computing Local Thermal Equilibrium (LTE) stellar atmosphere models. The specific form of the source function, required by the algorithm, is obtained through a linear expansion of the Planck function around a trial temperature distribution. The correct solution is quickly obtained via an iterative correction procedure. The nonmatricial structure, which is the distinctive feature of the implicit intergral method, offers the possibility to take into account a very large number of frequency, angle, and depth discrete points, without any penalty in terms of numerical or computational problems.